1. Field of the Invention
The present invention relates to an image forming apparatus and an image forming method for generating a halftone image forming the halftone dots in accordance with an inputted multi-level gray-scale image.
2. Description of the Related Art
An electro-photographic image recording apparatus such as a copier or a laser beam printer using an electro-photographic method is well known as a high speed, high quality image forming apparatus. With the progress of digital technology in recent years, there is a growing demand for an electro-photographic image recording apparatus with higher image quality from the POD market to the office or home consumer market. Particularly in the high end market, there is a further growing demand for images undergoing a screen process such as printing. A screen process is a process for generating a color gradations with the number of color dots (color lines) or the density, not mixing the colors, such as in a paint. The human eye has a characteristic that a color looks thinner at a lower density of color dots, and the color looks denser at a higher density. Using this characteristic, the density of a color dot is controlled for each of yellow, magenta, cyan and black, and a full color is represented by combining the color dots (color lines).
The electro-photographic image recording apparatus records the image by exposing an image carrier to light, such as a laser beam, and can form all images from a binary image such as a character to an image including halftones such as a photograph. In regenerating a halftone, an image processing method such as a pulse width modulation method (PWM method), a dithering method or an error diffusion method is employed. Various patterns can be formed on an image carrier by use of such processing methods. The charged toner particles are attached to an obtained pattern on the image carrier, transferred to a transfer member and fixed, whereby the final output image can be obtained. Four colors of cyan (C), magenta (M), yellow (Y) and black (K) are generally used as the toner.
In the electro-photographic method, it is common that regular dither of dot intensive type is used to form the pattern by dithering. Dithering is a method for replacing the halftone with an aggregate of dots called halftone dots by binarizing the shading of an original image at a dither threshold value (threshold value formed in a predetermined pattern) according to a predetermined rule. With this method, since interference fringes (moiré) occur when halftone dots of four colors are superposed, a pattern in which an array of halftone dots has a different angle (screen angle) for each color of CMYK is created. The screen angle is the angle between the direction where the halftone dots are arranged and the vertical axis or the horizontal axis. Also, the number of halftone dots per unit length (how many halftone dots there are in an inch) is referred to as a screen line number. That is, the screen line number represents the fineness of halftone dots. As the screen line number increases (the number becomes larger), the halftone dots are less conspicuous to the naked eye, thereby providing printed matter of high quality. Conversely, as the screen line number decreases, the halftone dots are more conspicuous, giving a rough impression. In typical color printed matter, the screen angle is a combination of 15° for C, 75° for M, 0° for Y and 45° for K, and the screen line number is 133 or 175 lines. There are two methods, referred to as a rational tangent method and an irrational tangent method, for generating a pattern having a different screen angle for each color. The rational tangent method involves setting the tangent of the screen angle θ (tan θ) to be a rational number, and the irrational tangent method involves setting tan θ to be an irrational number.
However, in the typical rational tangent method, any screen angle or screen line number may not be realized in some cases, depending on the resolution of image. FIG. 4 is a view showing one example of a dither table with the rational tangent method. In FIG. 4, although the dither table is closest to a screen line number of 175 lines and a screen angle of 15° at a resolution of 600 dpi, the actual screen line number or angle is different from the ideal. On the contrary, with the irrational tangent method, there is an advantage that the screen angle or screen line number can be easily changed. FIG. 5 is a view showing one example of a halftone dot pattern 501. The halftone dot pattern 501 is held in a halftone dot pattern table in which dither threshold values (THx, THy) each representing one halftone dot are arranged in two dimensions, like a lattice. The halftone dot pattern table has a table length of D. FIG. 6 is a view showing the typical dithering with the irrational tangent method. The X axis and the Y axis of FIG. 6 represent the recording pixel coordinate axes of image data in the main scanning direction and the sub-scanning direction, and the U axis and the V axis represent the address coordinate axes of the halftone dot pattern. Reference numeral 601 denotes the print image data. The coordinates A (Ay, Ax) of the image data in the recording pixel coordinate system X-Y can be subjected to coordinate transformation into the coordinates A (Av, Au) of the halftone dot pattern in the address coordinate system U-V in accordance with the following expression.Au=(Ax·cos θ+Ay·sin θ)·p Au=(Ax·cos θ+Ay˜sin θ)·p Av=(−Ax·sin θ+Ay˜cos θ)˜p p=table length D of halftone dot pattern table/(resolution/screen line number)
At this time, p is the address coordinate conversion value in the image data of one pixel.
Using the above expression, the recording pixel coordinate system X-Y of the image data is transformed into the address coordinate system U-V of the halftone dot pattern. Further, an arbitrary screen angle or screen line number can be easily achieved with only one halftone dot pattern, using the residual value divided by the table length D of the halftone dot pattern table.
A technique as disclosed in U.S. Pat. No. 5,235,435 is a typical example of this irrational tangent method. However, in the irrational tangent method it is well known that there is a dispersion in the area of halftone dots formed at the same density depending on a variation in the correlation between the position of lattice points of the halftone dot pattern and the recording pixel position of the image data. Since this dispersion causes a periodic unevenness in the image, leading to an image defect, a method for adding a random number to the address coordinate has been proposed (e.g., refer to Japanese Patent Laid-Open No. S55-6393 (1980) and Japanese Patent Laid-Open No. S61-137473(1986)). However, with the above method using a random number, though the dispersion in the area of a formed halftone dot can be suppressed, there is a problem that irregularities in the halftone dots are likely to occur. Therefore, a method for correcting the address coordinate with the deviation amount by calculating the amount of deviation between the recording pixel coordinate and the address coordinate at a predetermined reference point in each unit dot area and correcting the amount of deviation depending on the distance between the reference point and the lattice point of the dot pattern has been proposed (e.g., refer to Japanese Patent Laid-Open No. H06-30276(1994)).
FIG. 16A shows an example of the halftone dots in which all of the deviation amount is not corrected (U.S. Pat. No. 5,235,435). Since the deviation amount is not corrected in this example, the area of the halftone dot is greatly different for each dot. As a result, even if the image before binarization has a certain density, the image after binarization contains a local change in the density. On the other hand, FIG. 16B shows an example of the halftone dots in which all the deviation amount is corrected (refer to Japanese Patent Laid-Open No. 6-30276(1994)). In this example, the area of all the halftone dots is the same, but the interval between the halftone dots is different. For example, the interval 2 is longer by one pixel than the interval 1 in FIG. 16B.
However, with the method as disclosed in Japanese Patent Laid-Open No. 6-30276(1994), it is required that the obtained deviation amount is interpolated with the distance between the above predetermined reference point and the lattice point of the halftone dot pattern. Further, the deviation amounts at a plurality of points may be used in some cases, resulting in a problem that the computation cost is increased accordingly. Also, if the areas of the halftone dots are perfectly matched, a specific pattern may occur in the low density area or the high density area at a longer period than the halftone dots, possibly leading to an image defect.